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Remarks on Laplacian of graphical models in various graphs. (English) Zbl 1485.05106

Nielsen, Frank (ed.) et al., Geometric science of information. 5th international conference, GSI 2021, Paris, France, July 21–23, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12829, 685-692 (2021).
Summary: This paper discusses the connection between inverses of graph Laplacians with the diagonal increased by a positive vector and the covariance matrices of associated Gaussian graphical models.
Afterwards we study the way of modification of a graph Laplacian on the case of daisy graphs.
For the entire collection see [Zbl 1482.94007].

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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References:

[1] Nakashima, H., Graczyk, P.: Wigner and Wishart Ensembles for graphical models. arXiv:2008.10446 [math.ST] (2020)
[2] Brouwer, AE; Haemers, WH, Spectra of Graphs (2011), New York: Springer, New York · Zbl 1231.05001 · doi:10.1007/978-1-4614-1939-6
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